suspension (changes)

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The suspension is the universal way to make points into paths.

The suspension of a type $A$ is the higher inductive type $\Sigma A$ with the following generators

- A point $\mathrm{N} : \Sigma A$
- A point $\mathrm{S} : \Sigma A$
- A function $\mathrm{merid}:A\to (N\mathrm{N}{=}_{\Sigma A}S\mathrm{S})$
~~\mathrm{merid}~~merid : A \to~~(N~~(\mathrm{N} =_{\Sigma A}~~S)~~\mathrm{S})

The suspension of a type $A$ is a the pushout of $\mathbf 1 \leftarrow A \rightarrow \mathbf 1$.

These two definitions are equivalent.

category: homotopy theory

Last revised on September 4, 2018 at 05:48:52. See the history of this page for a list of all contributions to it.